In past decades, there has been an upsurge in the development of three-dimensional (3D) shape measurement and its applications. Over the years, there are a variety of technologies developed including laser scanning, stereo vision, and structured light. Among these technologies, the structured-light technique has the advantages of fast computation speeds and high measurement resolution. Therefore, it has been extensively studied in this field of research. Nowadays, with the rapid development of digital devices, different kinds of patterns can be easily generated by a video projector. As a result, digital fringe projection (DFP), a variation of the structured light method, has had many applications owing to its speed and accuracy.

Typically, for a DFP system, ideal sinusoidal fringe pattern projection is required for high accuracy 3D information retrieval. Since traditional DFP projects 8-bit sinusoidal fringe patterns, it suffers from some major limitations such as the speed limit (e.g., 120 Hz), the requirement for nonlinear gamma calibration, and the rigid synchronization requirement between the projector and the camera. To overcome these limitations, the binary defocusing technology was developed which projects 1-bit square binary pattern and generates ideal sinusoidal pattern through projector defocusing.

In the past few years, the binary defocusing technique has shown great potential for many applications owing to its speed breakthroughs, nonlinear gamma calibration free and no rigid synchronization requirement between the camera and the projector. However, a typical square binary pattern suffers from some major limitations: (1) high-order harmonics, introduced by a square wave, which affect the accuracy of measurement, cannot be completely eliminated by projector defocusing; (2) a reduced measurement volume since the projector needs to be properly defocused to generate the desired high-quality sinusoidal patterns; and (3) difficulty achieving high-quality measurements with wider square binary patterns.

The binary dithering technique, originally developed for printing technology, is found to have great potential for overcoming these aforementioned limitations of the square binary method. However, the binary dithering technique, which simply applies a matrix operation to the whole image, still has great room for improvement especially when the fringe patterns are not sufficiently defocused. Although there have been past efforts made to improve the performance of dithering techniques for 3D shape measurement, those approaches are either computationally expensive or fail to improve the quality with different amounts of defocusing.

In this research, we aim at further improving the binary dithering technique by optimizing the dithered patterns in intensity domain. We have developed both global and local optimization frameworks for improving dithered patterns. Our simulation and experimental results have demonstrated that: the global optimization framework improves the Bayer-order dithering technique by approximately 25% overall and up to 50% for narrower fringe patterns (e.g. fringe period of T = 18 pixels); the local optimization framework can improve the performance of a more advanced error-diffusion dithering technique by 20% overall and up to 40% for narrower fringe patterns (e.g. T = 18 pixels). Moreover, since the local algorithm involves optimizing a small image block and building up the desired-size patterns using symmetry and periodicity, it is much faster in terms of optimization time than the global algorithm.